Pyjama problem¶
In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin the stripes are.
Core Idea¶
Pyjama problem is treated here as the recurring tiling theory identity summarized by this source-grounded definition: In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin the stripes are. In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin the stripes are.
Scope of Application¶
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Quantitative bounds. Let E(\varepsilon) := {z \in \mathbb{C}: \mathrm{Re}(z) \in (-\varepsilon, \varepsilon) \pmod{1}} be the pyjama stripe of width 2\varepsilon .
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Quantitative bounds. Noah Kravitz and James Leng proved that \exp\exp\exp(\varepsilon^{-O(1)}) rotations of E(\varepsilon).
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Quantitative bounds. about the origin are sufficient to cover \mathbb{C} , hence obtaining an explicit upper bound for the pyjama problem.
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Quantitative bounds. It remains an open problem to obtain lower bounds for the pyjama problem beyond the trivial volume preserving bound of \varepsilon^{-1}/2 .
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Documented setting. In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin.
Clarity¶
A clear use of Pyjama problem names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin the stripes are.
Manages Complexity¶
Pyjama problem compresses multiple tiling theory details into a stable diagnostic relation. The source shows both the central mechanism—the problem was posed in 2006 by Alex Iosevich, Mihail Kolountzakis, and Máté Matolcsi.—and the practical consequence—about the origin are sufficient to cover \mathbb{C} , hence obtaining an explicit upper bound for the pyjama problem. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.
Abstract Reasoning¶
- Type the carrier. Identify the tiling theory entities to which the claim applies.
- State the relation. Use the source-grounded identity: In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin the stripes are.
- Check operation and conditions. It was answered in the affirmative by Freddie Manners in 2015, using an analogy with Furstenberg’s ×2, ×3 Theorem.
- Demand recognition evidence.
Knowledge Transfer¶
Within the home domain. Knowledge about Pyjama problem transfers literally when a new case preserves the same carrier type, relation, and recognition test. Let E(\varepsilon) := {z \in \mathbb{C}: \mathrm{Re}(z) \in (-\varepsilon, \varepsilon) \pmod{1}} be the pyjama stripe of width 2\varepsilon . Noah Kravitz and James Leng proved that \exp\exp\exp(\varepsilon^{-O(1)}) rotations of E(\varepsilon). Beyond the home domain. No canonical parent is asserted for Pyjama problem.
Neighborhood in Abstraction Space¶
Pyjama problem sits in a sparse region of the domain-specific corpus (74th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Combinatorial Optimization & Discrete Structures (31 abstractions)
Nearest neighbors
- Strip packing problem — 0.85
- Filling radius — 0.83
- Coons patch — 0.83
- Terminal singularity — 0.83
- Julia set — 0.83
Computed from structural-signature embeddings · 2026-10-08